What is the maximum surface charge density of aluminum? I understand that the maximum free charge carrier density for aluminum has been measured using the Hall effect (in the case of electric current). However, I'm not clear how to determine the maximum surface charge density to which aluminum (or any conductor) can be charged, assuming the neighboring medium does not breakdown. 
Say for instance we had a parallel plate capacitor with an idealized dielectric that could withstand infinite potential across it. What is the max surface charge density that the plates could be charged to? I assume that at some point all of the surface atoms are ionized. 
Is this simply the volumetric free carrier density multiplied by the atomic diameter?
 A: I think you can estimate the maximal surface charge density as follows. The energy needed to remove an electron from a solid to a point immediately outside the solid is called work function $W$. For aluminum $W$ is about $4.06-4.26$ eV. The thickness of the charged layer on the surface of a conductor is about several Fermi lengths
$$
\lambda_{F}=\left(  3\pi^{2}n_{e}\right)  ^{-1/3},
$$
where $n_{e}=N/V$ is the total electron number density for the conductor. I think that the charge starts to drain from the surface of a conductor when $E\lambda_{F}$ is of the order of the work function, where $E=4\pi\sigma$ is the electric field near the surface:
$$
eE\lambda_{F}=4\pi\sigma\left(  3\pi^{2}n_{e}\right)  ^{-1/3}\sim W,
$$
hence
$$
\sigma\sim\frac{W}{4e}\left(  \frac{3n_{e}}{\pi}\right)  ^{1/3}.
$$
About the question Yrogirg. I think that the question is not quite correct. The charge are distributed on the surface of a conductor in such a way that the electric potential is a constant in the body of the conductor. The «stability» of charge on the surface is greatly dependent on the geometry of the object in question. Sharp points require lower voltage levels to produce effect of charge «draining» from the surface, because electric fields are more concentrated in areas of high curvature, see, e.g. St. Elmo’s fire.
A: Given the work function from the answer above, no electron can get as close as 
$\frac{1}{4\pi\epsilon_0} e^2/r = 4.06eV$, at the range it would rather leave the aluminium than get closer to another electron.
A: There is no sensible answer to this question.
You can put any amount of charge on a blob of aluminum sitting in a vacuum, or surrounded by an ideal insulator. Why not?
If you put an awful lot of electrons on a blob of aluminum sitting in a vacuum, the electrons will eventually start shooting off by thermionic emission, and most of the excess charge will be gone after, let's say, 1 day. If you put even more electrons, most of them will be gone after 1 millisecond. But there is no "maximum" really, just a gradual speed-up of the discharging. Even 1 excess electron will not be stable for eternity.
If you subtract electrons instead of adding them, certainly nothing will happen. Well, I guess positively-charged atomic nuclei could fly off if the charge was significant enough. Again, this process does not let you say that a certain amount of charge is "the maximum possible", it's just a process that happens more and more frequently as the charge increases.
If you add or subtract an awful lot of electrons from a blob of aluminum surrounded by insulator, the insulator will eventually break down. If you have an ideal insulator that cannot break down, then nothing will happen no matter how many electrons are there.
You seem to have the idea that all electrons must come from surface atoms, so if you take away every electron from every surface atom, then it will be impossible to take away any more charge. But if you think about it, that's sort of a weird idea, when there's still all those electrons inside the metal! In fact, the idea is not correct. The "surface" where an insulator can store charge is not infinitesimal, nor necessarily exactly one atom thick. It's actually a depth equal to the so-called Debye length. If you subtract loads of electrons -- every electron from every "surface" atom -- the  Debye length will just increase allowing you to scrape electrons out of atoms residing farther and farther from the surface.
